Abstract

We have two populations: Pop I and Pop II. Pop I is normally distributed with unknown mean μ l and unknown variance σ 21 . Pop II is also normally distributed with unknown mean μ 2 and unknown variance σ 22 . We wish to do the following statistical test $$\mathop H\nolimits_0 :\mathop \sigma \nolimits_1^2 = \mathop \sigma \nolimits_2^2 $$ (20.1) verses $$\mathop H\nolimits_1 :\mathop \sigma \nolimits_1^2 \ne \mathop \sigma \nolimits_2^2 $$ (20.2) We collect a random sample of size n 1 from Pop I and let \(\overline {\mathop x\nolimits_1 } \) be the mean for this data and s 21 is the sample variance. We also gather a random sample of size \(\overline {\mathop x\nolimits_2 } \) is the mean for the second sample with s 22 the variance. We assume these two random samples are independent.KeywordsRandom SampleDecision RuleNormal PopulationStatistical InferenceSample VarianceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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